Random Matrices

Abstract

In Chap. 4, we apply methods and results from Chaps. 2 and 3 to random matrices. To include only results that are reasonably complete, we restrict our attention to the class of nonnegative matrices (that is, matrices whose entries are all nonnegative). Although there have been a great deal of results in this area in different directions (see [17] or [44]), here we restrict ourselves only to problems involving recurrence, tightness, invariantmeasures, and laws of large numbers for products of random matrices. The reason is, of course, our own bias and also the desire to avoid duplicating work already available in books or well-known papers.